1. Field of the Invention
The invention relates to a method for manufacturing an optical system having an optical axis and imaging a point P to a point P', both on the optical axis. The invention also relates to an optical system for imaging an object point P to an image point P'.
2. Description of the Related Art
The quality of the image formed at P' is generally expressed in terms of optical aberrations. The aberration theory of images generated by an optical system has been gradually developed from the seventeenth century on. Early analyses by e.g. Descartes, Roberval and Huygens concern the spherical aberration which arise when imaging an object point through a single refracting or reflecting surface. From this work we know the perfect or stigmatic imaging properties of conic sections (quadratic surfaces) and the so-called oval surfaces of Descartes (quartic surfaces). As a special case, the stigmatic points generated by a spherical surface are obtained (Huygens aplanatic points). Further research was oriented towards the spherical aberration generated by a single lens and later in the eighteenth century, the comatic aberration of off-axis pencils of rays. As a result, at the beginning of the nineteenth century, the as-designed quality of telescope objectives by Dolland and Fraunhofer was very good (well within the diffraction limit) and the actual optical quality of the instruments was mainly limited by manufacturing imperfections and material inhomogeneities. However, the numerical aperture and the field angle of these objective were rather small.
The need for an aberration theory valid for more complicated optical systems with larger values of numerical aperture and field angle was felt when photography emerged. The so-called third order aberration theory which, in principle covers both larger aperture and field angles was probably first developed by Petzval but his results remained unpublished. A comprehensive third order theory for optical systems with circular symmetry consisting of a arbitrary sequence of optical elements was published by L. von Seidel in 1856. As a rule of thumb, this approximate theory yields reliable results for numerical apertures up to 0.10 or even 0.15 while the field angle may amount to some ten degrees. The Seidel third order theory was of great help for the design of photographic objectives with the specifications of the second half of the past century. For the design of e.g. microscope objectives with a high numerical aperture, i.e. larger than 0.50, and a small field angle, the Seidel theory is not sufficient although it can produce a good design starting point.
In 1863, R. Clausius.sup.1 published a paper in which he shows under what condition an optical system (e.g. a mirror system) is able to concentrate radiant power in an optimum way even when the aperture of the imaging pencils is large. In 1874, H. Helmholtz.sup.2 showed that for correct imaging of a finite size object the so-called sine condition should be respected because otherwise the optical throughput or etendue of the optical system is not preserved from object to image space. But it is the name of E. Abbe.sup.3 which is generally associated with this sine condition because he was the first to establish the link between this condition and the freedom of comatic aberration of the imaging system even at large aperture.
In optical recording the exit plane of a semiconductor laser is imaged onto a record carrier through an objective lens. During operation of a record player, the image should follow tracks on the record carrier. To that end, the position of the image on the record carrier is varied by moving the objective lens in a plane perpendicular to its optical axis. Known objective lenses.sup.4 have been designed to comply with the sine condition in order to obtain the necessary large field. The image must be focused in the plane of the tracks. To maintain the correct focusing when the record carrier shows deflections in the direction of the optical axis, the objective lens is moved along the optical axis. However, at larger numerical apertures it has turned out to be difficult to maintain the quality of the image when following the axial deflections.